The aim here is to explain what quantum mechanics is, without falling into either of these traps. It will be presented as a series of points. The reader's aim should be to understand each point. If you're confused, read on - it may be that you can skip points entirely. On the other hand, there's a limit to what can be explained intuitively using animations. I'm going to plough through anyway. Enjoy.

On the left there is an equation. On the right, there is a wave that moves in a particular way - in this case, similarly to how a sound wave travels: The height of the graph here would be the pressure of a sound wave as it travels down a corridor.

The important thing is that on the left we have an equation. On the right, we have a behaviour.

The only thing to understand here is that each equation describes the behaviour of a wave. If you change the equation slightly, the way the wave moves is slightly different.

Following the pattern, the Schrödinger equation is on the left, and on the right we have a curve that moves in a particular way. It isn't the same way that water moves, and it isn't the same way that a sound wave moves, but it is quite simple.

Equations of this type describe how a curve moves. The Schrödinger equation is a simple equation, similar to a water wave equation or a sound wave equation.

The curve plotted on the right is called a wavefunction. (The absolute square of the wavefunction is plotted here.)

The less said about this the better - if it's not clear what's going on, play with the experiment until the relationship between the curve drawn on the graph, and the probable location of the electron is clear.

The wavefunction is the thing to focus on - you know it's a wave, and you know that it moves in a particular way. The thing to understand from this point is that it dictates where the electron would be most likely to be found if you did an experiment that could pinpoint it.

The gif below shows an electron moving freely in a square box. The darker the colour, the more likely the electron would be to be found at that position.

In the example above, the electron started off as a probability cloud in the middle, but moving to the right. As time goes on, it spreads out and collides with the walls of its enclosure.

In this experiment, we start off with the electron at the left, moving right. We put a barrier with two slits in its path. Then we see what happens.

If, for instance, you used the theory that an electron moves like a bouncy ball, it wouldn't produce the finger-like patterns.

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